Gravitational Fields

Question 1

What is a gravitational field?

Answer 1

it is an example of a field of force and is defined as force per unit mass

Question 2

Can you represent a gravitational field?

Question 3

For a point outside a uniform sphere, the mass of the sphere may be considered to be …

Answer 3

a point mass at its centre

Question 4

Recall Newton’s law of gravitation for the force between two point masses

Answer 4

F is proportional to the magnitude of the 2 masses
F is inversely proportional to the square of the distance between the 2 masses
F = Gm₁m₂ / r²

Question 5

How should you analyse circular orbits in gravitational fields?

Answer 5

relate the gravitational force to the centripetal acceleration it causes

Question 6

What key things do you need to understand about geostationary satellites? (4)

Answer 6

1. remains at the same point above the Earth’s surface
2. has an orbital period of 24 hours
3. orbits from west to east
4. orbits directly above the Equator

Question 7

Derive the equation for the gravitational field strength due to a point mass

Answer 7

g = F / m
F = Gm₁m₂ / r²
g = GM / r²

Question 8

Why is g approximately constant for small changes in height near the Earth’s surface?

Answer 8

Δr is not very large, relative to the quantity r

Question 9

Define gravitational potential at a point

Answer 9

the work done per unit mass in bringing a small test mass from infinity to the point

Question 10

Give the equation for the gravitational potential in the field due to a point mass

Answer 10

φ = –GM / r

Question 11

Recall the equation for gravitational potential energy between two point masses

Answer 11

Eₚ = –GMm / r

Question 12

Why is gravitational potential energy said to be negative?

Answer 12

The energy the object requires to go to infinity is positive - work would need to be done against the force due to gravitational attraction, as opposed to the system doing the work

Question 13

Define gravitational field intensity (or strength) at a point

Answer 13

the amount of force experienced by a mass of 1kg placed at that point

Question 14

Give an equation for gravitational field intensity, and state its units

Answer 14

E = F / m
gravitational field intensity = force / mass
units: N / kg

Question 15

Derive the relationship between gravitational field intensity and the distance between two point masses

Answer 15

E = F / m & F = GMm / r²
E = GM / r²
Since G and M are constants, E ∝ 1/r²